1. Go through it, apply for core, don't get accepted don't get $15k
2. Go through it, apply for core, don't get accepted to core but get $15k
3. Go through it, apply for core, get accepted to core, enter core, don't get $15k (but get more money, with strings)
4. Go through it, apply for core, get accepted to core, decline core, don't get $15k
Point is if you are accepted in to the core program then clearly you are good enough to get the $15k. But if you decide to NOT enter the core program, they seem to pull that $15k which clearly you are good enough for.
For some startups, they might actually prefer the no strings $15k over the more money and network but giving up equity.
Now of course YC is not obligated to give anyone $15k. But it seems they are pulling the $15k which they consider you at least good enough for, if you don't accept their terms. Which is again their right, though should be clear.